A bench of Chief Justice T S Thakur and Justice U U Lalit said the matter will be heard on March 29 after the vacation and will not be deleted after senior advocate Ram Jethmalani sought the urgent hearing.
The lawyer said the plea would become infructuous if the hearing does not take place as the person, who has become the CVC, would retire after "enjoying fruits of the appointment".
"Mr Jethmalani, you argue for bringing people out of jail," the bench said and later assured him that the plea would be heard on urgent basis.
Earlier, the court, on August 13, last year, had issued notice to the Centre and others on the plea challenging the appointment of the CVC and VC T M Bhasin. The plea was filed by NGO Common Cause through lawyer Prashant Bhushan.
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Jethmalani, who also appeared in the case supporting the plea, had sought the court's permission to inspect the records filed by the central government in this regard.
While Chaudhary was appointed as the CVC on June 6, this year, Bhasin took charge as the VC on June 11.
The PIL alleged that their appointments were "arbitrary, illegal and in violation of the principle of institutional integrity".
"The government did not even place the names of short- listed candidates in public domain or the fact that Chaudhary and Bhasin were being considered for the appointment to such important positions," the plea said.
filed by NGO Centre for Integrity, Governance and Training in Vigilance Administration, had on May 13 lifted its embargo and allowed the Centre to go ahead with the appointment of CVC and VC from the list of candidates shortlisted by it.
In December last year, the apex court had asked the Centre to take its prior "leave" before going ahead with appointments for which 10 candidates each were shortlisted after scrutinising 130 applications.